We have tides because of the gravitational pull of the moon. It is also known to affect human behaviour - hence the term lunatics - so why would it not also have an effect on water tables in the earth?
Whether it does affect gardening activities will never be resolved scientifically as there is no commercial interest in any of the big agri firms in doing so. We thus have to rely on anecdotal evidence form those who practise it over long periods and there is a wealth of old and new literature on the subject dating back to ancient Egyptian texts.
I suspect it's of importance to farmers and peasants with limted resources of machinery, fertiliser, weed killer, water for irrigation and so on who need to maximise their crop fertility but of far less import to those of us who garden in the developed world with plenty of resources. I would remind you though that our climate is changing, that population pressures, particularly in the south east, make water an increasingly precious and expensive resource. Unusual floods and droughts around the world mean this year's harvests are poor so fruit, corn and veg will be more expensive to buy and I suspect that one day rather more of us will be embracing old and new methods of making the most of our crops whilst limiting our impact on the planet's resources and ecology.
After all, it's not so many years ago that everyone thought going organic was bonkers and just look at how many of us avoid chemicals on our food crops and flowers for our own sake and for wildlife.